Abstract : The intense thermal energy flux emanating from the critical layer in laser-produced plasmas is shown to generate an instability that derives from the magnetic field dependence of the thermal conductivity. This implies that B fields, with their attendant nonuniform heating effects, will occur even in uniformly irradiated spherical pellets or plane slabs. These fields may play a role in attempts to compress pellets for fusion for example by being partially trapped and amplified by compression in the interior of a pellet. (Author)